Theorem expi

Description: An exportation inference. (Contributed by NM, 29-Dec-1992) (Proof shortened by Mel L. O'Cat, 28-Nov-2008)

	Ref	Expression
Hypothesis	expi.1	⊢ ( ¬ ( 𝜑 → ¬ 𝜓 ) → 𝜒 )
Assertion	expi	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		expi.1	⊢ ( ¬ ( 𝜑 → ¬ 𝜓 ) → 𝜒 )
2		pm3.2im	⊢ ( 𝜑 → ( 𝜓 → ¬ ( 𝜑 → ¬ 𝜓 ) ) )
3	2 1	syl6	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )